In the other direction all irreducible modules for \(\mathrm {Vir} \otimes t,t^{-1}]\)  with finite dimensional weight spaces were classified in [1]}. This result was generalised in [2]}, where author replaced \(t,t^{-1}]\)  by a finitely generated commutative associative unital algebra over \(.Very recently, for \) n 2\(, a partial classification result for the Lie algebra \) (Wn An) B\( is obtained in \cite {serpc}.\) This paper is concerned with irreducible representations of \(W_n \otimes B\)  and \((W_n \ltimes A_n) \otimes B\)  with finite dimensional weight spaces, where \(B\)  is a finitely generated commutative associative unital algebra over \(. We prove that any such module is a single pointevaluation module (see definition \ref {evd1}). In other words these modules are irreducible modules for \) Wn\( or \) Wn An\( and their complete classification is known \cite {ybvf, kgx}.\) As pointed out earlier that the irreducible modules for \(W_n\)  or \(W_n \ltimes A_n\)  with finite dimensional weight spaces will fall in two cases [3]} : one is uniformly bounded and the other one is
highest weight modules. Weights of uniformly bounded module form a translate of a full lattice (missing at most a one point); while weights of highest weight modules are truncated from above in the one direction.
